Dynamic behavior of mixed convection heat transfer among horizontal co-axial fixed pipes at varying temperatures: Efficiency of cylindrical heat sink

The aim of the current research is to highlight the time-dependent properties of laminar convective thermal transmission inside a semi-infinite pipe, with an emphasis on flow frequencies that impact inter-fluid momentum and energy. The implicit finite difference approach is used to solve two-dimensional mathematical model composed of nonlinear partial differential equations. The research includes forecasting thermal performance of time-dependent flow in a pipe over several parameter ranges relevant to the flow model. The obtained forecasts were emphasized graphically. The numerical solutions were separated into steady and unsteady components, with the steady component yielding findings that were then used to determine the time dependent surface shearness and energy shearness in the time dependent phase. The stable component of the investigation revealed that raising the buoyancy force parameter and the impact of viscous dissipation significantly improved the flow velocity pattern and heat distributions throughout the flow domain. While the amplitude of time dependent surface shearness varied somewhat across various buoyancy force parameter values, the amplitude of time dependent heat transmission rates varied significantly. This study sheds light on the interaction of several characteristics, such as buoyancy force effects and internal energy loss, on time-dependent thermal energy flow inside a semi-infinite pipe subjected to laminar convective flow. It is worth noting that the amplitude of the time dependent rate of heat transmission shows more noticeable variations with different values of the buoyancy force parameter, in contrast to the minute change in the amplitude of the time dependent surface sheerness.